Question

Find the area of a rectangle with length 3xpower 2-2and breadth 2x+5

Answer 1

Using the Pythagorean Theorem a2+b2=c2, we substitute the expressions into the equation:

x2+(2x+2)2=132
x2+4x2+8x+4=169
5x2+8x−165=0

Factor the equation:

(5x2−25x)+(33x−165)=0
5x(x−5)+33(x−5)=0
(5x+33)(x−5)=0

The two solutions we find are −335 and 5. Since we cannot have a negative width, we immediately discard the negative solution, leaving us with x=5.

Now we simply solve for the area by substituting x with 5, and we get our answer:

2(5)+2=10+2=12
5⋅12=60

Answer 2

Given,

For the rectangle

lenght = 3x² - 2

breadth = 2x + 5

•°• Area = length × breadth

= 3x² - 2 × 2x + 5

= 3x² - 4x + 5